Forward Euler Solutions and Weakly Invariant Time-Delayed Systems
This paper presents a necessary and sufficient condition for the weak invariance property of a time-delayed system parametrized by a differential inclusion. The aforementioned condition generalizes the well-known Hamilton-Jacobi inequality that characterizes weakly invariant systems in the nondelay...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/481853 |
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| Summary: | This paper presents a necessary and sufficient condition for the weak
invariance property of a time-delayed system parametrized by a differential inclusion.
The aforementioned condition generalizes the well-known Hamilton-Jacobi
inequality that characterizes weakly invariant systems in the nondelay setting. The
forward Euler approximation scheme used in the theory of discontinuous differential
equations is extended to the time-delayed context by incorporating the delay and
tail functions featuring the dynamics. Accordingly, an existence theorem of weakly
invariant trajectories is established under the extended forward Euler approach. |
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| ISSN: | 1085-3375 1687-0409 |